Subject:
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Re: LDraw Math Question??
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Newsgroups:
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lugnet.cad
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Date:
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Thu, 26 Sep 2002 22:31:52 GMT
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Viewed:
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1458 times
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In lugnet.cad, Kyle McDonald wrote:
> To me this is a left hand coordinate system. Which is fine.
> What I'm curious about is given the system above, when rotating
> about the Z axis by a positive angle, does the +X axis on the
> right swing up? or down?
>
> When rotating about the X axis by a positive angle, does the +Z
> that is near the user swing up? or down?
When rotating around X, +Y -> +Z. When rotating on Y, +Z -> +X. For Z,
it's +X -> +Y.
> Along with this, I have questions about the Matrices in the type 1
> lines. There are two conventions here; in some systems you transform
> a point as a column vector on the right side of the matrix (as in
> traditional matrix math and as used in the Foley & Van Dam textbook),
> while in some other systems you transform a point as a row vector on the
> left side of the matrix (as in the Newman & Sproull textbook). This is
> usually correlated with the choice of a right-handed vs. left-handed
> system, but not always.
>
> Does anyone know which method LDraw uses?
It doesn't matter (I think) - you get the same results either way.
Personally, I program with the vertices as a row vector on the left:
[x1 y1 z1 1] [xx yx zx 0]
[x2 y2 z2 1] [xy yy zy 0]
[... ] [xz yz zz 0]
[x y z 1]
where the first matrix is composed of all the triples in a files, and
the second matrix is built from the reference to that file:
1 clr x y z xx xy xz yx yy yz zx zy zz subfile.dat
I find this approach easier to wrap my mind around, especially when I'm
stacking all those triples into a single Nx4 array for processing.
> If a type 1 line is:
> 1 16 X Y Z A B C D E F G H I file.dat
>
> and a point in file.dat (x,y,z) then which of the following does LDraw use:
>
> A B C
> 1) x y z * D E F
> G H I
>
> A D G
> 2) x y z * B E H
> C F I
This is the closest, but LDraw doesn't actually use any of these. It
passes all the values around as individual parameters. But the math is:
x' = xA + yB + zC + X
y' = xD + yE + zF + Y
z' = xG + yH + zI + Z
> x A B C
> 3) y * D E F
> z G H I
>
> x A D G
> 4) y * B E H
> z C F I
These aren't allowed - matrix multiplication works on two arrays of size
AxB and BxC - the number of columns in array #1 has to equal the number
of rows in array #2.
HTHADNC,
Steve
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Message is in Reply To:
 | | LDraw Math Question??
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| Hi. I'm having a few problems with the LDraw coordinate/rotation system. I understand that LDraw 'world' coordinates follow the following: -X is on the left. +X is on the right. -Y is up +Y is down -Z is into the screen +Z is out of the screen To me (...) (24 years ago, 26-Sep-02, to lugnet.cad)
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